Wind Turbines

Question 1

What is the equation for power of wind blowing through an area?

Answer 1

P = 1/2 ρ A v^3

Question 2

What are the wind industry roughness classes?

Answer 2

0 - Water
0.5 - Flat land
1 - Agri-land with shallow hills
2 - Agri-land with Buildings
3 - Forest/Towns
4 - Cities

Question 3

What is the roughness length for class 0? What about for class 4?

Answer 3

0: z0 = 0.0002m
4: z0 = 1.6m

Question 4

What is the condition of a Weibull Distribution that causes it to be referred to as Rayleigh Distribution?

Answer 4

β = 2

Question 5

What does a Weibull Distribution represent?

Answer 5

The number of hours per year of each wind speed

Question 6

Where is there viscous flow around an aerofoil?

Answer 6

In the thin boundary layer

Question 7

How do pressure and shear stress act relative to the surface of an aerofoil?

Answer 7

Pressure is normal
Shear stress is tangential

Question 8

How are lift and drag defined in terms of the resultant force and freestream wind velocity?

Answer 8

Lift is the component of resultant perpendicular to velocity, Drag is parallel component

Question 9

Which surface of an aerofoil experiences suction resulting in lift?

Answer 9

The upper surface where velocity is higher

Question 10

What causes stall of an aerofoil?

Answer 10

Angle of attack increases to the extent that flow detaches from the upper surface

Question 11

Why are aircraft aerofoils unsuitable for wind turbines?

Answer 11

They are used at a lower Reynolds number than ideal
They are thicker than necessary for turbines

Question 12

What does the actuator disk model assume?

Answer 12

No mixing of air from adjacent turbines
Air is inviscid and incompressible
Total pressure is constant before and after the disk but not through it

Question 13

What is the equation for air velocity downstream of a wind turbine?

Answer 13

Uw = (1-2a)U∞ where U∞ is upstream velocity and a is axial flow induction factor

Question 14

What is the axial flow induction factor?

Answer 14

1 minus the ratio of pressure at the disk to pressure upstream

Question 15

What are the coefficients of power and thrust relative to axial flow induction factor a?

Answer 15

Cp = 4a(1-a)^2
Ct = 4a(1-a)

Question 16

What changes about the flow as it passes through the actuator disk?

Answer 16

It loses streamwise velocity
It gains rotation

Question 17

Why are actuator disk models used?

Answer 17

Simple
Low cost
Accurate

Question 18

What is the difference between angle of attack (α) and pitch (β)

Answer 18

Angle of attack is between the aerofoil centreline and the angle of wind approach
Pitch is between centreline and reference plane (horizontal vertical etc)

Question 19

What is the equation for flow angle Φ?

Answer 19

Φ = atan ((1-a)/(1+a’)LSR))

Question 20

How can the power generated by a wind turbine be expressed most simply?

Answer 20

Torque multiplied by rotational velocity of blades

Question 21

What is the equation for tangential induction factor a’?

Answer 21

(a(1-a))/(LSR)^2

Question 22

How do chord and twist typically vary along a turbine blade?

Answer 22

They decrease exponentially with radius down the blade

Question 23

What do the provided chord and twist equations assume?

Answer 23

Drag is negligible

Question 24

How is a linear taper blade designed?

Answer 24

A chord distribution is chosen which is tangential to the ideal distribution at a specified point

Question 25

Why are linear taper designs used?

Answer 25

They are more cost-effective to design and build

Question 26

What are the limitations of BEMT?

Answer 26

Doesn’t account for tip losses
Has to assume a is uniform along the blade

Question 27

What is the LSR with no tip losses?

Answer 27

TSR * r/R

Question 28

What is the BEMT equation for iterating phi?

Answer 28

phi = atan [(1-a)/((1+a’)LSR)]

Question 29

What is the equation for S in the BEMT equations?

Answer 29

cot phi (aka. 1/tan phi)

Question 30

For the sake of simplifying the BEMT we can define a term X. What is X?

Answer 30

sqrt(1+S^2)

Question 31

How is alpha obtained for Cl(alpha) and Cd(alpha)?

Answer 31

alpha = phi - ideal twist angle ‘beta’

Question 32

Both of the BEMT equations give their solutions as fractions. How are the fractions different for a and a’?

Answer 32

For a the denominator is 1-a, for a’ it is 1+a’. Both have the respective a as the numerator

Question 33

What term, Y, precedes both BEMT equations?

Answer 33

Bc/(8pi r) where c is chord distribution

Question 34

Using the simplifications X and Y, what is the BEMT equation for a?

Answer 34

Y * X * (ClS + Cd)

Question 35

Using the simplifications X and Y, what is the BEMT equation for a’?

Answer 35

Y * X/S * (Cl - CdS)

Question 36

What is the actuator disk model?

Answer 36

A representation of a turbine as a 1D disk with swept area Ad